The scope of the for loop defines what is done for each file. Everything after the for loop is only done once:

 import os                                                                   
 import glob                                                                 
 os.chdir('C:\Users\U2970\Documents\Arcgis\Text_files\Data_exports')         
 for file in list(glob.glob('*.txt')):                                       
     reader = open(file)               # <-- Things done for each file

 # Things done only once:                      
 from EXPORT_COLUMN_SET import *                                             

 try:                                                                        
      data = column_set(reader)                                              
      data.start_data_printer()                                              
 finally:                                                                    
      reader.close()   

You can indent the rest of the code to put it inside the for loop:

 import os                                                                   
 import glob                                                                 
 os.chdir('C:\Users\U2970\Documents\Arcgis\Text_files\Data_exports')       
 for file in list(glob.glob('*.txt')):                           
     reader = open(file)                  # ^                 
                                          # |                
     from EXPORT_COLUMN_SET import *      # |              
                                          # | Things now done for each file
     try:                                 # |                                 
          data = column_set(reader)       # |                              
          data.start_data_printer()       # |                              
     finally:                             # |                              
          reader.close()                  # v